Question

What is the arc length of the shaded region to the nearest tenth?

Answer 1

285

Explanation:

The total amount of degrees in a circle is 360, we know that the un-shaded portion of the circle is 90 degrees this means that the shaded portion has 270 degrees.

We also know that the area of the circle is
`\pi r^(2)` but we are finding a portion of that, therefore we would need to multiply it by
`((270)/(360) )`. The radius is also given which is 11.

Area of the shaded region =
`((270)/(360)) * \pi 11^(2)` = 285

Answer 2

Given that the unshaded arch formed a right angle with radius 11, the arc length of the shaded region is 17.3.

How to calculate the arc length of the shaded region

To calculate the arc length of the shaded region, determine the angle formed by the unshaded arc.

Since it forms a right angle with the radius of the circle, we know that it is a quarter of the circumference of the circle.

The formula for the circumference of a circle is given by:

Circumference = 2 * π * radius

In this case, the radius is 11 cm.

Substitute the value into the formula

Circumference = 2 * π * 11

Circumference = 22 * π

To find the arc length of the shaded region, which is a quarter of the circumference, divide the circumference by 4:

Arc Length = (22 * π) / 4

Arc Length = 5.5 * π

Using an approximation of π as 3.14, calculate the arc length:

Arc Length ≈ 5.5 * 3.14

Arc Length ≈ 17.27

Rounding to the nearest tenth, the arc length of the shaded region is approximately 17.3 units.

Therefore, the arc length of the shaded region is 17.3 (to the nearest tenth).